Standard Deviation Method or Z-score Method: Calculating Safety Stock with Statistical Accuracy

Discover how this statistical approach helps businesses determine the optimal level of inventory to mitigate uncertainties and ensure smooth operations.

Understanding the Standard Deviation Method or Z-score Method: 

The Standard Deviation Method, also known as the Z-score Method, is a statistical technique used to calculate safety stock. It involves analyzing historical demand data and assessing the variability or volatility in demand. By quantifying this variability, businesses can determine the additional inventory buffer needed to meet unexpected demand fluctuations.

How does it work? 

Let’s break down the steps involved in using the Standard Deviation Method or Z-score Method:

  • Collect historical demand data: Gather historical demand data for the item or product under consideration. This data should cover a representative period, typically several months or years.
  • Calculate average demand: Find the average or mean demand over the selected period. This provides a baseline to compare deviations from the average.
  • Calculate standard deviation: Determine the standard deviation of the demand data. The standard deviation measures the dispersion or spread of the demand values around the average. A higher standard deviation indicates greater demand variability.
  • Determine the desired service level: Define the desired service level, which represents the level of customer demand satisfaction the business aims to achieve. Common service level targets include 95%, 97.5%, or 99%. A higher service level implies a lower risk of stock outs.
  • Calculate the Z-score: The Z-score is calculated based on the desired service level. It represents the number of standard deviations necessary to achieve the desired service level. Value of Z can be taken from this table as per service level.
  • Determine lead time: Identify the lead time, which is the time between placing an order and receiving it. This can include order processing time, manufacturing time, and transportation time.
  • Multiply the Z-score by the square root of lead time and the standard deviation of daily demand: 

The formula for calculating safety stock is

                                                   Safety Stock = Z-score × √(Lead Time) × Standard Deviation of Daily Demand.


Let’s consider an example to illustrate the Standard Deviation Method or Z-score Method:

Suppose you have historical demand data for a particular product over the past 12 months. The average daily demand is found to be 200 units, and the standard deviation is calculated as 30 units. You aim for a service level of 95%. Assuming a lead time of 10 days and the safety stock can be calculated as follows:

Safety Stock = Z-score × √(Lead Time) × Standard Deviation of Daily Demand
Safety Stock = 1.64 × √(10) × 30
Safety Stock ≈ 155.58 units.


In this example, to achieve a 95% service level with a lead time of 10 days and a standard deviation of daily demand of 30 units, a safety stock of approximately 155.58 units is recommended.

Benefits of the Standard Deviation Method or Z-score Method:

  • Utilizes statistical data analysis to calculate safety stock.
  • Considers historical demand variability to ensure adequate inventory buffer.
  • Provides a quantitative approach to balance service levels and inventory costs.
  • Enables businesses to make informed decisions based on data-driven insights.


The Standard Deviation Method or Z-score Method offers a statistical approach to calculate safety stock, considering historical demand variability. By incorporating this method into inventory management practices, businesses can achieve optimal stock levels, minimize stockouts, and enhance customer satisfaction.